Abstract

Fabrication tolerances can significantly degrade the performance of fabricated photonic circuits and process yield. It is essential to include these stochastic uncertainties in the design phase in order to predict the statistical behaviour of a device before the final fabrication. This paper presents a method to build a novel class of stochastic-based building blocks for the preparation of Process Design Kits for the analysis and design of photonic circuits. The proposed design kits directly store the information on the stochastic behaviour of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using these macro-models, only a single deterministic simulation is required to compute the stochastic moments of any arbitrary photonic circuit, without the need of running a large number of time-consuming circuit simulations thereby dramatically improving simulation efficiency. The effectiveness of the proposed approach is verified by means of classical photonic circuit examples with multiple uncertain variables.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. X. Chen, M. Mohamed, Z. Li, L. Shang, and A. R. Mickelson, “Process variation in silicon photonic devices,” Appl. Opt. 52, 7638–7647 (2013).
    [Crossref] [PubMed]
  2. D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).
    [Crossref]
  3. Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).
    [Crossref] [PubMed]
  4. A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).
    [Crossref]
  5. D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.
  6. A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.
  7. M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
    [Crossref]
  8. P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).
    [Crossref]
  9. T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).
    [Crossref] [PubMed]
  10. Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
    [Crossref]
  11. T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).
  12. R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).
    [Crossref]
  13. Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).
    [Crossref]
  14. D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).
    [Crossref]
  15. “Aspic from Filarate srl,” http://www.aspicdesign.com . Accessed: 30-10-2017.
  16. M. S. Eldred, “Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design,” AIAA Paper 2274, 37 (2009).
  17. D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).
    [Crossref]
  18. D. Xiu, Numerical methods for stochastic computations: a spectral method approach (Princeton University Press, 2010).
  19. D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
    [Crossref]
  20. J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.
  21. J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.
  22. P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.
  23. P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).
    [Crossref]
  24. D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).
    [Crossref]
  25. Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
    [Crossref]
  26. A. Papoulis, “Random variables and stochastic processes,” (McGraw-Hill, 1985).
  27. X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
    [Crossref]
  28. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach Optical Filter Design and Analysis: A Signal Processing Approach (Wiley Online Library, 1999).
  29. A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for wdm systems,” J. Lightwave Technol. 20, 296–303 (2002).
    [Crossref]

2018 (1)

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
[Crossref]

2017 (4)

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).
[Crossref]

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).
[Crossref] [PubMed]

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).
[Crossref]

2016 (1)

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
[Crossref]

2015 (1)

2013 (4)

X. Chen, M. Mohamed, Z. Li, L. Shang, and A. R. Mickelson, “Process variation in silicon photonic devices,” Appl. Opt. 52, 7638–7647 (2013).
[Crossref] [PubMed]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).
[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).
[Crossref]

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).
[Crossref]

2012 (3)

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
[Crossref]

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).
[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

2009 (1)

M. S. Eldred, “Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design,” AIAA Paper 2274, 37 (2009).

2003 (1)

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).
[Crossref]

2002 (2)

D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).
[Crossref]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for wdm systems,” J. Lightwave Technol. 20, 296–303 (2002).
[Crossref]

1996 (1)

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[Crossref]

1993 (1)

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).
[Crossref]

Antonini, G.

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).
[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

Augustin, F.

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
[Crossref]

Bakker, A.

Bogaerts, W.

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
[Crossref]

Canavero, F. G.

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).
[Crossref]

P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.

Canciamilla, A.

Cassano, D.

D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.

Chen, X.

Chrostowski, L.

Daniel, L.

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).
[Crossref] [PubMed]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).
[Crossref]

De Zutter, D.

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).
[Crossref]

Dhaene, T.

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
[Crossref]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).
[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

Eldred, M. S.

M. S. Eldred, “Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design,” AIAA Paper 2274, 37 (2009).

Elfadel, I. M.

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).
[Crossref]

El-Moselhy, T. A.

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).
[Crossref]

Ferranti, F.

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

Flueckiger, J.

Ghanem, R.

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).
[Crossref]

Gilg, A.

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
[Crossref]

Ginste, D. V.

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).
[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

Hmaidi, A.

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
[Crossref]

Jhoja, J.

Karniadakis, G. E.

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).
[Crossref]

D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).
[Crossref]

Klein, J.

Knockaert, L.

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).
[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

Le Lourec, P.

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[Crossref]

Le Maître, O.

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).
[Crossref]

Leijtens, X.

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[Crossref]

Li, A.

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
[Crossref]

Li, Z.

Liu, A.

Lu, Z.

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach Optical Filter Design and Analysis: A Signal Processing Approach (Wiley Online Library, 1999).

Manfredi, P.

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).
[Crossref]

P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.

Martinelli, M.

Marzouk, Y.

Melati, D.

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).
[Crossref]

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).
[Crossref]

A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.

Melloni, A.

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).
[Crossref]

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).
[Crossref] [PubMed]

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).
[Crossref]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for wdm systems,” J. Lightwave Technol. 20, 296–303 (2002).
[Crossref]

A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.

D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.

Mickelson, A. R.

Mohamed, M.

Morichetti, F.

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).
[Crossref]

D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.

Papoulis, A.

A. Papoulis, “Random variables and stochastic processes,” (McGraw-Hill, 1985).

Pond, J.

Preibisch, J. B.

J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.

J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.

Roncelli, D.

Schuster, C.

J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.

J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.

Shang, L.

Smit, M.

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[Crossref]

Soares, F. M.

Sochala, P.

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).
[Crossref]

Spanos, P. D.

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).
[Crossref]

Spina, D.

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
[Crossref]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).
[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

Stievano, I. S.

P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.

Su, Z.

Triverio, P.

J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.

J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.

Villegas, M.

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
[Crossref]

Wang, X.

Waqas, A.

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).
[Crossref]

A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.

Weng, T.-W.

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).
[Crossref] [PubMed]

Wever, U.

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
[Crossref]

Xing, Y.

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
[Crossref]

Xiu, D.

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).
[Crossref]

D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).
[Crossref]

D. Xiu, Numerical methods for stochastic computations: a spectral method approach (Princeton University Press, 2010).

Ye, Y.

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
[Crossref]

Zhang, Z.

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).
[Crossref] [PubMed]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).
[Crossref]

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach Optical Filter Design and Analysis: A Signal Processing Approach (Wiley Online Library, 1999).

Adv. Water Resources (1)

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).
[Crossref]

AIAA Paper (1)

M. S. Eldred, “Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design,” AIAA Paper 2274, 37 (2009).

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).
[Crossref]

IEEE Trans. Components Packaging Manufacturing Technol. (1)

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).
[Crossref]

IEEE Trans. Computer-Aided Design Integrated Circuits Systems (1)

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).
[Crossref]

IEEE Trans. Electromagnetic Compatibility (1)

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).
[Crossref]

IEEE Trans. Microwave Theory Techniques (2)

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).
[Crossref]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).
[Crossref]

J. Comput. Phys. (1)

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).
[Crossref]

J. Lightwave Technol. (3)

Math. Computers Simulation (1)

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).
[Crossref]

Nanophotonics (1)

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

Opt. Express (2)

Photonics Res. (1)

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).
[Crossref]

Probabilistic Engineering Mechanics (1)

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).
[Crossref]

SIAM J. Sci. Comput. (1)

D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).
[Crossref]

Other (9)

D. Xiu, Numerical methods for stochastic computations: a spectral method approach (Princeton University Press, 2010).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach Optical Filter Design and Analysis: A Signal Processing Approach (Wiley Online Library, 1999).

D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.

A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.

“Aspic from Filarate srl,” http://www.aspicdesign.com . Accessed: 30-10-2017.

J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.

J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.

P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.

A. Papoulis, “Random variables and stochastic processes,” (McGraw-Hill, 1985).

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Figures (9)

Fig. 1
Fig. 1 (a) Typical approach for the stochastic analysis of photonic circuit exploiting standard process design kits, Monte Carlo simulations and nonintrusive generalized polynomial chaos approximation. (b) Computation of the stochastic behaviour of the circuit exploiting the proposed stochastic process design kits. In both cases PDK and stochastic PDK are circuit independent.
Fig. 2
Fig. 2 (a) Connection of two standard building blocks. (b) Connection of equivalent augmented building blocks where each port is scaled by factor (M+1).
Fig. 3
Fig. 3 (a) Schematic of the second-order Mach-Zehnder filter (b) Transfer function of the Mach-Zehnder filter at the bar (black) and the cross (red) ports for the nominal design. The thin grey lines show the effect of fabrication uncertainties on the waveguide widths and the gap of couplers.
Fig. 4
Fig. 4 Comparison between (a) the mean and (b) the standard deviation of the magnitude of bar (black) and cross (red) ports of the filter obtained with BB-gPC (blue dashed-dotted line), MC analysis (solid line) and the classical gPC method (circles). The MC analysis is carried out using 104 samples.
Fig. 5
Fig. 5 PDF of the intensity transfer function at the (a) bar (black) and (b) cross (red) ports of the filter at a centre wavelength 1.5502 μm respectively. (c) PDF of the 3-dB bandwidth at the bar port of the filter. Blue dash-dot line: PDF computed using the BB-gPC. Full line: PDF computed using MC technique. Circles: PDF computed using the classical gPC method. For all three methods 104 samples are used.
Fig. 6
Fig. 6 (a) Schematic of the fifth-order ring filter (b) Transfer function of the ring filter at drop (black) and through (red) ports for the nominal design. The thin grey lines show the effect of fabrication uncertainties on the waveguide widths.
Fig. 7
Fig. 7 Comparison between (a) the mean and (b) the standard deviation of the magnitude of drop (black) and through (red) ports of the filter obtained with BB-gPC (blue dashed-dotted line), MC analysis (solid line) and the classical gPC method (circles). The MC analysis is carried out using 104 samples.
Fig. 8
Fig. 8 (a) PDF of the intensity of (a) the drop port and (b) the through port of the filter at a centre wavelength 1.55025 μm (c) PDF of the 3-dB bandwidth at the drop port of the filter. Blue dash-dot line: PDF computed using the BB-gPC. Full line: PDF computed using the MC analysis. Circles: PDF computed using the classical gPC method. For all three method 104 samples are used.
Fig. 9
Fig. 9 (a) Group delay of the coupled ring resonator filter at the drop port. (b) The standard deviation of the group delay at the drop port of the filter. The blue dash-dot line represents the proposed technique. The full line shows the result of MC analysis using 104 samples. The circles represents the results obtained using the classical gPC method.

Tables (1)

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Table 1 Efficiency of BB-gPC

Equations (17)

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Y ( ξ ) = i = 0 y i ϕ i ( ξ ) .
ϕ i ( ξ ) , ϕ j ( ξ ) = Ω ϕ i ( ξ ) ϕ j ( ξ ) W ( ξ ) d ξ = a i δ i j
Y ( ξ ) = i = 0 M y i ϕ i ( ξ ) ,
M + 1 = ( N + P ) ! N ! P ! .
b = S a ,
i = 0 M b i ϕ i ( ξ ) = i = 0 M j = 0 M S i a j ϕ i ( ξ ) ϕ j ( ξ ) ,
Ψ S i = R ,
b p k = i = 0 M j = 0 M S i a j ϕ i ( ξ ) ϕ j ( ξ ) , ϕ p ( ξ ) ,
b PC = S PC a PC ,
b 0 ϕ 0 + b 1 ϕ 1 = S 0 a 0 ϕ 0 ϕ 0 + S 1 a 0 ϕ 1 ϕ 0 + S 0 a 1 ϕ 0 ϕ 1 + S 1 a 1 ϕ 1 ϕ 1 .
b 0 = S 0 a 0 ϕ 0 ( ξ ) ϕ 0 ( ξ ) , ϕ 0 ( ξ ) + S 1 a 0 ϕ 1 ( ξ ) ϕ 0 ( ξ ) , ϕ 0 ( ξ ) + S 0 a 1 ϕ 0 ( ξ ) ϕ 1 ( ξ ) , ϕ 0 ( ξ ) + S 1 a 1 ϕ 1 ( ξ ) ϕ 1 ( ξ ) , ϕ 0 ( ξ ) .
b 1 = S 0 a 0 ϕ 0 ( ξ ) ϕ 0 ( ξ ) , ϕ 0 ( ξ ) + S 1 a 0 ϕ 1 ( ξ ) ϕ 0 ( ξ ) , ϕ 1 ( ξ ) + S 0 a 1 ϕ 0 ( ξ ) ϕ 1 ( ξ ) , ϕ 1 ( ξ ) + S 1 a 1 ϕ 1 ( ξ ) ϕ 1 ( ξ ) , ϕ 1 ( ξ ) .
S PC = [ S PC 00 S PC 01 S PC 10 S PC 11 ] ,
S PC 00 = S 0 ϕ 0 ( ξ ) ϕ 0 ( ξ ) , ϕ 0 ( ξ ) + S 1 ϕ 1 ( ξ ) ϕ 0 ( ξ ) , ϕ 0 ( ξ ) , S PC 01 = S 0 ϕ 0 ( ξ ) ϕ 1 ( ξ ) , ϕ 0 ( ξ ) + S 1 ϕ 1 ( ξ ) ϕ 1 ( ξ ) , ϕ 0 ( ξ ) , S PC 10 = S 0 ϕ 0 ( ξ ) ϕ 0 ( ξ ) , ϕ 1 ( ξ ) + S 1 ϕ 1 ( ξ ) ϕ 0 ( ξ ) , ϕ 1 ( ξ ) , S PC 11 = S 0 ϕ 0 ( ξ ) ϕ 1 ( ξ ) , ϕ 1 ( ξ ) + S 1 ϕ 1 ( ξ ) ϕ 1 ( ξ ) , ϕ 1 ( ξ ) .
μ ( λ ) = S PC 00 ( λ ) ,
σ ( λ ) = i = 1 M S PC i 0 ( λ ) ϕ i ( ξ ) ϕ j ( ξ ) .
S ( λ ) = i = 1 M S PC i 0 ( λ ) ϕ ( ξ ) .

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